Q53. - Algebra 1

Question

GEOMETRY If $\Delta LMN$ is similar to $\Delta LPO$, what is z?

F 240

G 140

H 120

J 70

Step-by-Step Solution

Answer

 The value of z is 140.   

Step 1. Use the definition of similar triangles.

Two triangles are similar if they have the same ratio of corresponding sides and equal pairs of corresponding angles.

Since If $\Delta LMN$ is similar to $\Delta LPO$

We have

 $\frac{LN}{LO}=\frac{LM}{LP}=\frac{MN}{OP}$

Step 2. Solve for the missing side.

As the triangles are similar to each other, and we have

 $\frac{LN}{LO}=\frac{LM}{LP}=\frac{MN}{OP}$

To find $OP=z$, we plug the values and simplify as shown

 $\begin{array}{l} \frac{180}{360}=\frac{70}{z}\text{ [Cross-multiply]}\\ 180\left(z\right)=70\left(360\right)\\ 180z=25200\end{array}$

We further simplify, by dividing 180 both sides as shown:

 $\begin{array}{l}\frac{180z}{180}=\frac{25200}{180}\\ z=140\end{array}$

Step 3. Interpret the result.

The missing side $OP=z$ has a measure of 140.